Run and tumble particle under resetting:a renewal approach

We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.Comment: 16 pages, 1 figure, version accepted in Journal of Physics

Movement-induced orientation: a potential mechanisms of cartilage collagen network morphogenesis

Articular cartilage is a layer of tissue lining the articulating osseous ends in diarthroidal joints. Its primary function is to provide a durable, low friction, load-bearing surface. Cartilage on cartilage, lubricated with synovial fluid, has a coefficient of friction of 0.02–0.005 (Charnley 1959), and regularly provides problem-free performance for a lifetime. Although this may not seem so remarkable, comparison to synthetic bearings is quite revealing. The coefficient of friction for steel on steel lubricated with oil is 0.1 (Jones 1936) and that of dry Teflon on Teflon is 0.04 (Bowden and Tabor 1950). Furthermore, the life of mechanical bearings is often less than 20 years. Articular cartilage is an exceptional material with an optimal design for its function